Finite-time Ruin Probability of Aggregate Gaussian Processes

#### K. Debicki, E. Hashorva, Lanpeng Ji, Zhongquan Tan

2014, v.20, №3, 435-450

ABSTRACT

Let ${\sum_{i=1}^n \lambda_i X_i(t) - g(t), t \in [0,T]}$ be an aggregate Gaussian risk process with a trend $g(t)$. We derive exact asymptotics of the finite-time ruin probability given by $$P(\sup_{t\in[0,T]} (\sum_{i=1}^n \lambda_i X_i(t) - g(t)) > u)$$ as $u \to \infty$ for $X_i(t), t \in [0,T], i\leq n,$ satisfying some asymptotic conditions. Further, we derive asymptotic results for the finite-time ruin probabilities of risk processes perturbed by an aggregate Gaussian process.

Keywords: ruin probability,Gaussian process,perturbed risk process,Levyprocess,(sub- and bi-)fractional Brownian motion,risk aggregation,subexponential risks